Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter logistic function.
logistic2_gradient_2(x, theta, delta)logistic2_hessian_2(x, theta, delta)
logistic2_gradient_hessian_2(x, theta, delta)
Gradient or Hessian of the alternative parameterization evaluated at the specified point.
numeric vector at which the function is to be evaluated.
numeric vector with the two parameters in the form
c(eta, phi).
value of delta parameter (either 1 or -1).
The 2-parameter logistic function f(x; theta) is defined here as
g(x; theta) = 1 / (1 + exp(-eta * (x - phi)))
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi) and eta > 0. Only eta and phi
are free to vary (therefore the name) while vector c(alpha, delta) is
constrained to be either c(0, 1) (monotonically increasing curve) or
c(1, -1) (monotonically decreasing curve).
This set of functions use a different parameterization from
link[drda]{logistic2_gradient}. To avoid the non-negative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta).
Note that argument theta is on the original scale and not on the log scale.